A sociologist thinks that middle school boys spent less time studying in 1981 than middle school boys do today. A study was conducted in 1981 to find the time that middle school boys spent studying on weekdays. The results (in minutes per weekday) are shown below.
Recently a similar study was conducted. The results are shown below.
At α = 0.05, do middle school boys study more today than in 1981? You can assume that the population approaches a normal distribution.
Transcribed Image Text:### Data Table for Educational Analysis
Below is a data table consisting of numerical values arranged in six rows and six columns. This table might represent different statistical values or measurements for educational purposes:
| Col 1 | Col 2 | Col 3 | Col 4 | Col 5 | Col 6 |
|-------|-------|-------|-------|-------|-------|
| 44.7 | 55.0 | 49.4 | 51.3 | 45.4 |
| 47.2 | 41.1 | 42.2 | 54.8 | 50.0 |
| 47.1 | 51.0 | 43.0 | 42.9 | 49.8 |
| 51.5 | 52.8 | 49.6 | 39.0 | 48.6 |
| 54.6 | 44.7 | 47.2 | 40.2 | 47.9 |
| 58.0 | 46.7 | 52.0 | 48.7 | 54.4 |
| 45.5 | 41.1 | 46.6 | 45.6 | 50.0 |
### Explanation of the Table
- **Rows and Columns:** The table is composed of six rows and six columns, indicating that it has a total of 25 numerical data points.
- **Data Values:** Each cell in the table contains a numerical value. These values might represent different parameters depending on the educational context in which they are used.
### Possible Uses in Education
- **Statistical Analysis:** The data can be used to teach basic statistical concepts such as mean, median, mode, range, and standard deviation.
- **Comparison:** Each column might represent a different category or variable, allowing students to perform comparative analyses.
- **Data Visualization:** The table can be converted into different types of graphs or charts like bar graphs, line charts, or scatter plots for better visualization and understanding.
### Graphs or Diagrams
There are no specific graphs or diagrams provided along with this table. However, educators are encouraged to use data visualization tools to create graphical representations of the data for a more comprehensive educational experience. Possible diagrams that can be created
Transcribed Image Text:Below is a data table featuring numerical values spread across eight rows and six columns. The specific context or subject matter related to these values is not provided.
| 31.9 | 32.1 | 39.1 | 36.6 | 24.2 |
|------|------|------|------|------|
| 38.8 | 21.9 | 36.2 | 26.9 | 35.5 |
| 33.8 | 28.0 | 35.4 | 31.9 | 29.6 |
| 27.7 | 37.1 | 36.8 | 36.9 | 28.5 |
| 35.4 | 28.7 | 30.5 | 34.3 | 34.2 |
| 35.9 | 30.0 | 32.6 | 33.0 | 35.7 |
| 28.7 | 33.8 | 30.2 | 41.1 | 25.3 |
This table presents a collection of values in a structured format, allowing for easy comparison and analysis across different rows and columns. Each cell contains a distinct number, which could represent a wide range of data types such as measurements, scores, or other quantitative information.
Graphical representation is not provided in this case, but if a graph or diagram were included, it might show trends, comparisons, or distributions of the values listed. For example, a line graph could plot these values to show changes over time or comparisons across different categories. Similarly, a bar chart could represent the same data in a visual format, with each bar corresponding to the values in one row or column.
To interpret this table effectively, understanding the context and units of measurement for the data is crucial. This information would provide insights into the significance of the differences and similarities among the numbers.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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